Models and calibration approaches for soil solution electrical conductivity using time domain
reflectometry
by Michael Christopher Mullin
A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Land
Resources and Environmental Sciences
Montana State University
© Copyright by Michael Christopher Mullin (2000)
Abstract:
Monitoring ionic solutes in soils is necessary to understand transport processes and to enable effective
managerial decisions regarding application and remediation of soil applied chemicals. Soil solution
electrical conductivity (ςw) is directly related to ionic solute concentration (Cr) and thus is useful as a
surrogate measurement. Time domain reflectometry (TDR) has shown promise for assessing ionic
solute distributions and has a number of advantages over other established methods; however,
calibration models must be invoked to estimate ςw using TDR. Three models and four calibration
approaches to obtain soil-specific model coefficients were investigated in this study for their efficacy to
infer ςw based on TDR measurements of bulk soil electrical conductivity (ςa) and volumetric soil water
content (θ). Two types of laboratory experiments were performed: a static (no flow) soil column
factorial matrix, and miscible displacement through soil columns under steady and transient water flow
conditions. Model parameters were determined from laboratory experiments in conjunction with the
various calibration methods by optimization of model estimated ςw against measured ςw from soil
solution extracts or effluent fractions. Model parameters that were determined from laboratory
experiments for a Flathead sandy loam soil were then used to generate predictions of ςw under field
conditions and results were compared with measurements obtained from soil solution extracts. Some
calibration model/method combinations resulted in excellent agreement with independently measured
ςw, although different combinations of . optimized model parameters (i.e. non-unique solutions)
provided substantially different agreement with independent measurements for both laboratory and
field trials. An apparent relationship was found between procedures used to acquire baseline .
measurements (field, laboratory) and for model calibration (laboratory). Results of this study are
potentially useful for those considering use of TDR for research or management applications.
r MODELS AND CALIBRATION APPROACHES FOR SOIL SOLUTION
ELECTRICAL CONDUCTIVITY USING TIME DOMAIN REFLECTOMETRY
by .
Michael Christopher Mullin
A thesis submitted in partial fulfillment
of the requirements for the degree
of
Master of Science
in
Land Resources and Environmental Sciences
MONTANA STATE UNIVERSITY
Bozeman, Montana
January 2000 '
ii
riyti
APPROVAL
of a thesis submitted by
Michael Christopher Mullin
This thesis has been read by each member of the thesis committee and has been found to
be satisfactory regarding content, English usage, format, citations, bibliographic style, and
consistency, and is ready for submission to the College of Graduate Studies.
//T-/QO
Jon M. Wraith
Committee Chair
Date
Approved for the Major Department
Jeffrey S. Jacobsen
Department Head
•
(Signature)
^
Date
Approved for the College of Graduate Studies
Bruce R. Mcleod
Graduate Dean
(Signature)
Date
Vo0
Ill
STATEMENT OF PERMISSION TO USE
In presenting this thesis in partial fulfillment o f the requirements for a master’s degree at
M ontana State University-Bozeman5 I agree that the Library shall make it available to
borrowers under rules o f the Library.
I f I have indicated my intention to copyright this thesis by including a copyright notice
page, copying is allowable only for scholarly purposes, consistent with “fair use” as
prescribed in the U.S. Copyright Law. Requests for permission for extended quotation from
or reproduction o f this thesis in whole or in parts may be granted only by the copyright
holder.
Signature
Date
ACKNOWLEDGMENTS
I would like to take this opportunity to thank my advisor, Dr. Jon Wraith for his
assistance with all aspects o f my research project. His professionalism is greatly
appreciated. I am grateful to Dr. Bhabani Das for his technical assistance and his
willingness to answer my numerous questions in a patient, thoughtful manner. Many
thanks to my other committee members, Drs. W illiam Inskeep and Paul Hook for lending
their time and effort to this project. Thanks to Rosie Wallander and Chris Wright for
statistical assistance. Were it not for the help o f student laborers Katie and Emily Davies,
I might still be taking electrical conductivity measurements and digging out from under a
pile o f dirty dishes. Thanks to them. Lastly, my family deserves credit for helping to
provide me with a foundation that has enabled me to pursue my goals.
vi
TABLE OF CONTENTS
Page
1. INTRODUCTION............. :........................................................................................... I
Electrical Conductivity in Soils...............................................................................2
Overview of Time Domain Reflectometry..............................................................4
Thesis Objective...................................................................................................... 8
References Cited...................................................................................................... 9
2. APPLICATION OF TWO CONDUCTOR-BASED MODELS FOR
SOIL SOLUTION ELECTRICAL CONDUCTIVITY................ ,.............................. 13
Introduction............................................................................................................ 13
Materials and Methods........ ................................................................................. 15
Two-Conductors Calibration Models................
15
Determination of Model Coefficients...........................................................17
Laboratory Calibration Experiments.............................................................19
Soil Column Matrix...................................................
20
Steady Flow Experiments....................................................................23
Transient Flow Experiments................................................................25
Results and Discussion..........................................................................................26
References Cited.................................................................................................... 39
3. PREDICTING SOIL SOLUTION ELECTRICAL CONDUCTIVITY UNDER
LABORATORY AND FIELD CONDITIONS............................................................ 43
Introduction.............................................
43
Materials and Methods..............................
;..45
Theoretical Background...........................................................................;....45
Laboratory Calibration Experiments............................................................ 48
Field Study............................................................................
51
Results and Discussion..................................... !.................................................. 52
Laboratory Calibration of Model Parameters.................. ;.......................... 52
Application of Laboratory Calibrations Results to Field D ata.....................58
References Cited........................................................................................... 67
4. SUMMARY.................................................................................................................. 70
vii
LIST OF TABLES
Table
Page
Chapter 2
1.
Calibration methods used for determination of R76 and R89
model coefficients.................................................................. :.................... 19
2.
Primary particle size fractions for Flathead SL and Amsterdam
SiCL soils......................................................................................................20
3.
Selected flow and salinity attributes for steady flow soil
column experiments......................................................................................24
4.
Selected flow and salinity attributes for transient wetness
soil column experiments...............................................................................25
5.
Best fit parameters for factorial soil column matrix experiments
using R76 and R89 models for soil solution electrical conductivity
in Flathead SL and Amsterdam SiCL soils...................................................28
6.
Best fit R76 and R89 model parameters from soil column flow
experiments for Flathead SL and Amsterdam SiCL soils.....................
7.
35
Correlation coefficients (r) for R76 and R89 parameter values reported
in Tables 5 and 6 ...........................................................................................36
Chapter 3
1.
Primary particle size fractions for Flathead SL and Amsterdam
SiCL soils......................................................................................................49
2.
Calibration methods used for determination of R76 and R89
model coefficients.........................................................................................50
3.
Selected flow and salinity attributes for steady flow soil
column experiments....................... :.............................................................52
Viii
LIST OF TABLES continued
4.
Selected flow and salinity attributes for transient wetness
soil column experiments............................................. !............................... 52
5.
Measured van Genuchten (1980) soil water retention parameters
for Flathead and Amsterdam soils, using a two-step
optimization process.................................................................. ................. 53
6.
Best fit MF model parameter (3 for all experiments and calibration
approaches........................................................................................... ....... 54
LIST OF FIGURES
Figure
Page
Chapter 2
I.
Measured results for repacked Flathead soil column matrix calibration
experiment. Linear fit for each 0 series shown for illustrative
purposes only, as a single value of R76 and R89 model
parameters were determined for the entire data se t..................................... 30
2., Measured results for repacked Amsterdam soil column matrix calibration
. experiment. Linear fit for each 0 series shown for illustrative
purposes only, as a single value of R76 and R89 model
parameters were determined for the entire data se t.....................................30
3.
Top: Two parameter sets obtained using calibration Method 4 for
the intact Flathead soil with the R76 model. Bottom: predicted
c?w for the intact Flathead soil (transient flow BTC) based on the
two sets of best fit R76 model parameters in top panel...............................34
4.
Fitted (optimized) ctwfor transient flow BTC using best fit method 2
parameters from R76 and R89 models for intact Flathead soil...................37
5.
Fitted (optimized) ctwfor transient flow BTC using best fit method 2
parameters from R76 and R89 models for repacked Amsterdam soil......... 37
Chapter 3
1.
Predicted ctwfor the intact Flathead SL soil using the MF model with
best fit parameters obtained from 5 different experiments. Measured
data is from transient flow miscible displacement experiment....................55
2.
Predicted ctwfor the repacked Amsterdam SiCL soil using the MF model with
best fit parameters obtained from 4 different experiments. Measured
data is from transient flow miscible displacement experiment....................56
3.
TDR estimates of ctwat 0.15 m depth in Flathead SL soil using the R76
model with best fit parameters determined from soil matrix
experiments (Method I). KNOg hand-applied on day 170.........................60
X
LIST OF FIGURES continued
4.
TDR estimates o f <tw at 0.15 m depth in Flathead SL soil using the R89
model with best fit parameters determined from soil matrix
experiments (Method I). KNO 3 hand-applied on day 1 70........................... 61
5.
TDR estimates o f a w at 0.15 m depth in Flathead SL soil using the MF
model with best fit parameters determined from soil matrix
experiments (Method I). KNO 3 hand-applied on day 1 7 0 ........................... 62
6.
TDR estimates o f ctw at 0.15 m depth in Flathead SL soil using the R76
model w ith best fit parameters determined from transient BTC
experiment (Method 2). KNO 3 hand-applied on day 170............................. 63
7.
TDR estimates o f Gw at 0.15 m depth in Flathead SL soil using the MF
model with best fit parameters determined from transient BTC
experiment (Method 2). KNO 3 hand-applied on day 170............................. 64
xi
ABSTRACT
Monitoring ionic solutes in soils is necessary to understand transport processes and
to enable effective managerial decisions regarding application and remediation o f soil
applied chemicals. Soil solution electrical conductivity (g w) is directly related to ionic
solute concentration (Cr) and thus is useful as a surrogate measurement. Time domain
reflectometry (TDR) has shown promise for assessing ionic solute distributions and has a
number o f advantages over other established methods; however, calibration models must
be invoked to estimate Gw using TDR. Three models and four calibration approaches to
obtain soil-specific model coefficients were investigated in this study for their efficacy to
infer Gw based on TDR measurements o f bulk soil electrical conductivity (G a) and
volumetric soil water content (0). Two types o f laboratory experiments were performed:
a static (no flow) soil column factorial matrix, and miscible displacement through soil
columns under steady and transient water flow conditions. Model parameters were
determined from laboratory experiments in conjunction with the various calibration
methods by optimization o f model estimated Gw against measured Gw from soil solution
extracts or effluent fractions. Model parameters that were determined from laboratory
experiments for a Flathead sandy loam soil were then used to generate predictions o f Gw
under field conditions and results were compared with measurements obtained from soil
solution extracts. Some calibration model/method combinations resulted in excellent
agreement with independently measured g w, although different combinations o f .
optimized model parameters (i.e. non-unique solutions) provided substantially different
agreement with independent measurements for both laboratory and field trials. An
apparent relationship was found between procedures used to acquire baseline .
measurements (field, laboratory) and for model calibration (laboratory). Results o f this
study are potentially useful for those considering use o f TDR for research or management
applications.
r
I
CHAPTER I
INTRODUCTION
The effects o f agricultural and other land use practices on surface and groundwater
quality is a major concern, regionally and nationally. Accurate measurements o f soil
physical attributes such as water content (0) and electrical conductivity (a) are critical to
monitoring the fate and transport of soil-applied chemicals such as fertilizer salts. As an
index o f salinity, a can be used to detect the presence and magnitude o f ionic solutes. A
technique known as time domain reflectometry (TDR) has made possible the unattended,
simultaneous measurement o f in situ 0 and bulk electrical conductivity (<ja) within the
same sample volume (Dalton, 1992). This unique ability o f TDR provides an attractive
alternative to convential time-consuming and often destructive procedures.
Many important chemical and physical processes in soil-water systems, such as
transport and bioavailability o f chemicals, are characterized more accurately by soil
solution electrical conductivity (g w) or resident solute concentrations in the soil solution
(Cr) than by measurements o f the bulk soil (e.g. a a). The response o f plants to salinity
effects are also more strongly correlated to a w than Ga. Substantial effort has gone
towards identifying relationships between Ga and Gw or Cr in soil-water systems (Gupta
and.Hanks, 1972; Rhoades et ah, 1976; Shainberg et al., 1980; Nadler and Frenkel, 1980;
Bohn et al., 1982, Rhoades et al., 1989; Nadler, 1982; Nadler, 1997). Extending the
solute measurement capabilities o f TDR will require reliable means o f relating, measured
i
2
(?a to c w or Cr, and this has been an active area o f research (e.g. Ward et ah, 1994;
Vanclooster et ah, 1994; Mallants et ah, 1996; Risler et ah, 1996; Persson, 1997; Vogeler
et ah, 1997; Persson and Bemdtsson, 1998; Wraith and Das, 1998; Das et ah, 1999).
Finding a universal calibration technique that will work well for all types o f soils under
variable water flow regimes would constitute a definite advancement. Whether or not a
universal calibration technique for all applications may be found, evaluation o f alternative
approaches under different soil and experimental conditions will advance our knowledge
and abilities in this area.
Electrical Conductivity in Soils
The electrical conductivity associated with dissolved ions in the pore water (c w)
accounts for the primary contribution to c a for most soils. The remaining contribution is
attributed to ions adsorbed to clay and other solid surfaces (a s). Bohn et ah (1982) and
others have reported that a w is proportional to the sum o f moles o f ion charge:
Ow = ^ X iMiIviI
[1]
i=l
where k is the cell constant o f the electrode, Xj is the molar-limiting ion conductivity (can
be obtained from tabled values), Mj is the ion molar concentration, V i is the value o f the
ion charge, and i denotes ionic species. While it is known that the magnitude o f o s is
dependent upon the amount and type(s) o f clay present (Cremers and Laudelout, 1966),
there is no direct (non-destructive) technique available for o s measurement. Rhoades et
ah (1976) suggested that o s could be determined from extrapolation o f the a w-a a curve to
3
CJw = 0, and later (Rhoades et aL, 1989) presented an empirical relation based on clay
content. Other methods for obtaining a s based on physical/empirical relationships exist
and are presented in Nadler and Frenkel (1980). Rhoades et al. (1989) believe that a
continuous conductance pathway along solid surfaces is unrealistic; instead, they
indicated that Gs is coupled in series with an electrical conductance element associated
with water-filled pores that bridge adjacent particle surfaces. The magnitude o f electrical
current flow through the continuous pore water pathway is dependent upon Gw and a
geometry factor (Fg) related to the tortuous nature o f flow paths (e.g. Rhoades et al., 1976;
Bohn et al., 1982). Fg is known to be a function o f 0 but has been described in various
ways (Archie, 1942; Rhoades et al., 1976; M ualem and Friedman, 1991).
There are a number o f techniques available for in situ Ga measurement (TDR, 4electrode sensors, electromagnetic induction sensors); however, there currently appear to
be no reliable methods available to directly measure Gw in situ. Thus, the electrical
conductivity o f a solution extract obtained from a saturated soil paste is the standard
measurement used for appraising soil salinity (USD A-ARS, 1954; Slavich and Petterson,
1990). For a large number o f samples, this is a time consuming process relative to other
estimates, such as obtaining extracts at higher 9 ratios, or inferring Gw from TDR
measurements o f Ga and 0. A limitation o f using 1:1 or 1:5 extracts is that the measured
value o f g w may not be representative o f Gw under field moisture conditions. Reitemeier
(1946) reported that for five o f six loam soils o f arid or semi-arid origins, total dissolved
salts, which are linearly related to Gw (Tanji and Biggar, 1972; Griffin and Jurinak, 1973;
4
M arion and Babcock, 1976), increased 2- to 9-fold upon dilution from field-moist to
500% wetness. The increase in TDS upon dilution for the five soils was attributed
primarily to dissolution o f sparingly soluble salts (Reitemeier, 1946).
Overview o f Time Domain Reflectometrv
TDR is essentially a form o f ‘cable radar’, as discontinuities along a transmission
line can be detected by analysis o f a reflected electromagnetic signal. The TDR technique
has been historically associated with mining, construction, and telecommunications
industries and was first adapted for use in soil science for measuring 0 about two decades
ago (Davis and Annan, 1977; Topp et ah, 1980). Topp et al. (1980) obtained an empirical
third order polynomial relationship between 0 and the soil apparent dielectric constant (s)
which is measured by TDR travel time analysis:
0 =-5.3X10"2 +2.9X10-2s -5.5X10^ s 2 +4.3X10"6s 3
[1]
Dalton et al. (1984) later demonstrated that Ga could be determined using TDR based on
the attenuation o f the TDR pulse by the medium o f interest, using the same probes.
A thin-section approach credited to Giese and Tiemann (1975) is commonly used to
determine Ga using TDR and has been shown to produce excellent results (e.g. Tbpp et
al., 1988; Nadler et al., 1991). The Giese and Tiemann equation as reported by Topp et
al. (1988) can be written as:
8 cZ ^
—I
V LZu A Vf
where the constants so and c are the permittivity o f flee space (8.854 X IO"12 F m '1) and
5
the velocity o f electromagnetic waves in free space (2.997 X IO8 m s'1), L is length (m) o f
the TDR probe, and Z0 and Zu are the characteristic probe impedance (Q) and output
impedance from the TDR cable tester (usually 50 Q). V0 and Vf are the initial and final
(after multiple signal reflections have died out) signal voltages, which may be determined
from the cable tester output signal. The ratio V0ZVf is directly proportional to the TDR
signal attenuation across the embedded probe, which is the basis for measurement o f <Ja
by the TDR technique. The product s0c is equivalent to (HO ti)"1 and has units o f Q '1.
Thus Eq. [2] can be written as:
v
2Vo - I
H0,iLZ,XVf
[3]
or more commonly as:
HO tiLZ t
[4]
where Z l = Zu/[(2V0ZVf) -1 ] is the measured resistive impedance load (Q) across the
embedded TDR probe. The term Z0Z(HOnL) can be equated to a probe constant (K0)
related to TDR probe geometry and impedance (Heimovaara, 1992; Baker and Spaans,
1993). K0 is normally determined by immersing the TDR probe in one or more solutions
o f known a:
*
Ix
where a ref is the known a o f a reference solution, and fp is a temperature correction
coefficient used to normalize the reference solution measurement to a standard
[5]
6
temperature (often 25°C). An empirical, salt specific relationship can be used to calculate
ff:
I
fx ~ ! + P ( T - T s)
[6]
with the measurement (T) and standard (Ts) temperatures in 0C and P about 0.02 for
many common salts.
TDR has excellent spatial and temporal measurement resolution, and is an
essentially non-destructive sampling technique. Other advantages o f the TDR technique
include the capability for automated measurement and for multiplexing sensors; that is,
obtaining measurements from multiple probes at multiple locations with a single TDR
instrument. Currently, the initial cost o f obtaining a TDR system appears to be the major
limitiation to a more widespread use o f this technology (Noborio et ah, 1994). However,
Ward (1994) noted that for certain applications, when costs such as sample analyses
associated with conventional techniques are accounted for, TDR may be less expensive in
the long-run. There are potential disadvantages o f using TDR in certain situations. For
example, it is difficult to obtain 0 at very high salinity (ow) levels [greater than about 14
to 20 dS m '1, depending on 0 (Dalton, 1992)] due to extensive attenuation of the TDR
signal. However, a w would be expected to reach this magnitude only under highly saline
conditions. Accurate TDR measurement o f 0 in soils that exhibit cracking can be
problematic due to the possibility o f air gaps forming between the probe and soil (Annan,
1977; Zegelin et al., 1992). In a limited number o f situations (soils very high in ash,
organic matter, or clay) it may become necessary to determine a soil-specific calibration
7
relationship in order to accurately determine 0 (Zegelin et a l, 1992; Bridge et al., 1996).
This is not a difficult process, but is somewhat time-consuming. Temperature effects
should be corrected for when cra is measured at temperatures other than the standard
reference (25°C). Heimovaara (1995) and Persson and Bemdtsson (1998) reported a a
temperature dependence similar to that for pure solutions. There is some debate as to the
need to correct for cable resistance (RcaBie) influences on TDR a a measurements.
Heimovaara (1995) found that IfR caBie was unaccounted for, TDR significantly
underestimated cra above 2.5 dS m"1 when using a 3 m coaxial cable. Because RcaBie
increases as cable length increases and diameter decreases, there may be a need to
account for RcabIe under certain conditions.
Most salinity research to date has been conducted using methods other than TDR primarily the four-electrode probe. While this technology is still in use, Nadler et al.
(1991), and others have advocated the use o f TDR for Ga measurement because o f its
many advantages. For example, the four-electrode probe is quite sensitive to quality o f
contact with the soil, while the attenuation o f the TDR signal is considered less sensitive
to soil-probe contact (Nadler et al., 1991).
Due to the soil specific nature o f the relationship between 0, Ga, and g w, relating
TDR measurements (G a and 0) to Gw requires calibration. Many physical/conceptual
calibration models have been proposed along with numerous methods for obtaining the
necessary model coefficients.
8
Thesis Obiective
The primary objective o f this study was to compare three models to describe the
relationships between Ca and a wunder variable 0 in soils, and four calibration approaches
to obtain the required soil-specific model parameters. Two popular conductor-based
conceptual calibration models were evaluated and results presented in Chapter 2.
Experiments and calibration techniques were designed to test these models under a
diverse set o f conditions, with the primary objective to further elucidate their utility in
estimating ctw for transient soil wetness conditions. Model parameters determined from
each calibration technique were compared relative to their abilities to provide estimates in
agreement with independently measured laboratory breakthrough curves (BTCs) for KCl
solutions. These miscible displacement BTCs were measured under steady and non­
steady (transient) water flow conditions. Chapter 3 contains an analysis o f a soil
hydraulic property-based calibration model using the same experiments and procedures as
described in Chapter 2. In addition, coefficients determined for all three physical/
conceptual models were applied to predict Gw in the root zone o f an agricultural crop
(peppermint: Mentha piperita L.), using 0 and Ga measured at multiple locations with
TDR. Based on the experiments performed, recommendations are provided regarding the
potential utility o f specific models and calibration procedures under different
combinations o f soil and transport conditions.
9
References Cited
Annan, A.P. 1977. Time domain reflectometry-air gap problems for parallel wire
transmission lines. GeoL Survey o f Canada, Paper 77-1B, 59-62.
Archie, G.E. 1942. The electrical resistivity log as an aid in determining some reservoir
characteristics. Trans. Am. Inst. Min. Metall. Pet. Eng. 146:54-62.
Baker, J.M., and E.J.A. Spaans. 1993. Comments on “Time domain reflectometiy
measurements o f water content and electrical conductivity o f layered soil columns”.
Soil Sci. Soc. Am. J. 57:1395-1396.
Bohn, H.L., J. Ben-Asher, H.S. Tabbara, and M. Marwan. 1982. Theories and tests o f
electrical conductivity in soils. Soil Sci. Soc. Am. J. 46:1143-1146.
Bridge, B.J., J. Sabburg, K.O. Habash, J.A.R. Ball, and N.H. Hancock. 1996. The
dielectric behaviour o f clay soils and its application to time domain reflectometiy.
Aust. J. Soil Res. 34:825-835.
Cremers, A.E., and H. Laudelout. 1966. Surface mobilities o f cations in clays. Soil Sci.
Soc. Am. Proc. 30:570-576.
Dalton, F.N. 1992. Development of time-domain reflectometiy for measuring soil w ater'
content and bulk soil electrical conductivity, p. 143-167. In G.C. Topp, W.D.
Reynolds, and R.E. Green (ed.) Advances in measurement o f soil physical properties:
Bringing theory into practice. SSSA Spec. Publ. 30. ASA, CSSA, and SSSA,
Madison, WL
Dalton, F.N., W.N. Herkelrath, D.S. Rawlins, and J.D. Rhoades. 1984. Time-domain
reflectometiy: simultaneous measurement o f soil water content and electrical
conductivity with a single probe. Science 224:989-990.
Das, B.S., J.M. Wraith, and W.P. Inskeep. 1999. Soil solution electrical conductivity
and nitrate concentrations in a crop root zone estimated using time-domain
reflectometiy. Soil Sci. Soc. Am. J. 63 (6):in press
Davis, J.L., and A.P. Annan. 1977. Electromagnetic detection o f soil moisture: progress
report I. Can. J. Remote Sensing 1:76-86.
Giese, K., and R. Tiemann. 1975. Determination o f the complex permittivity from thinsample time domain reflectometiy: Improved analysis o f the step response
waveform. Adv. Mol. Relax. Processes 7:45-59.
10
Griffin, R A ., and J.J. Jurinak. 1973. Estimation o f activity coefficients from the
electrical conductivity of natural aquatic systems and soil extracts. Soil Sci.
116:26-30.
Gupta, S.C., and R. J. Hanks. 1972. Influence o f water content on electrical conductivity
o f the soil. Soil Sci. Soc. Am. Proc. 36:855-857.
Heimovaara, T.J. 1992. Comments on “Time domain reflectometry. measurements o f
water content and electrical conductivity o f layered soil columns”. Soil Sci. Soc. .
Am. J. 56:1657-1658.
Heimovaara, T.J., A.G. Focke, W. Bouten, and J.M. Verstraten. 1995. Assessing
temporal variations in soil water composition with time domain reflectometry. Soil
Sci. Soc. Am. J. 59:689-698.
Mallants, D., M. Vanclooster, N. Toride, J. Vanderborght. M. Th. van Genuchten, and J.
Feyen. 1996. Comparison o f three methods to calibrate TDR for monitoring solute
movement in undisturbed soil. Soil Sci. Soc. Am. J. 60:747-754.
Marion, G.M., and K.L. Babcock. 1976. Predicting specific conductance and salt
concentration in dilute aqueous solutions. Soil Sci. 122:181-187.
Mualem, Y., and S.P. Friedman. 1991. Theoretical prediction o f electrical conductivity
in saturated and unsaturated soil. Water Resour. Res. 27:2771-2777.
Nadler, A. 1982. Estimating the soil water dependence o f the electrical conductivity
soil solution/electrical conductivity bulk soil ratio. Soil Sci. Soc. Am. J. 46:722-
726.
Nadler, A. 1991. Effect o f soil structure on bulk electrical conductivity (ECa) using
the TDR and 4P techniques. Soil Sci. 152:199-203.
Nadler, A. 1997. Discrepancies between soil solute concentration estimates obtained
by TDR and aqueous extracts. A u st J. Soil Res. 35:527-537.
Nadler, A., S. Dasberg, and I. Lapid. 1991. Time domain reflectometry measurements
o f water content and electrical conductivity o f layered soil columns. Soil Sci. Soc.
Am. J. 55:938-943.
Nadler, A., and H. Frenkel. 1980. Determination o f soil solution electrical conductivity
from bulk soil electrical conductivity measurements by the four-electrode method.
Soil Sci. Soc. Am. J. 44:1216-1221.
11
Noborio, K., K.J. Mclnnes, and J.L. Heilman. 1994. Field measurements o f soil
electrical conductivity and water content by time-domain reflectometry. Comp.
Electron. Agric. 11:131-142.
Persson, M. 1997. Soil solution electrical conductivity measurements under transient
conditions using time domain reflectometry. Soil ScL Soc. Am. J. 61:997-1003.
Persson, M. and R. Bemdtsson. 1998. Texture and electrical conductivity effects on
temperature dependency in time domain reflectometry. Soil Sci. Soc. Am. J.
62:887-893.
Reitemeier, R F . 1946. Effect o f moisture content on the dissolved and exchangeable
ions of soils o f arid regions. Soil Sci. 61:195-214.
Rhoades, J.D., N A . Manteghi, P.J. Shouse, and W.J. Alves. 1989. Soil electrical
conductivity and soil salinity: new formulations and calibrations. Soil Sci. Soc.
Am. J. 53:433-439.
Rhoades, J.D., P.A.C. Raats, and R.J. Prather. 1976. Effects o f liquid-phase electrical
conductivity, water content, and surface conductivity on bulk soil electrical
conductivity. Soil Sci. Soc. Am. J. 40:651-655.
Risler, P.D., J.M. Wraith, and H.M. Gaber. 1996. Solute transport under transient flow
conditions estimated using time domain reflectometry. Soil Sci. Soc. Am. J.
60:1297-1305.
Shainberg, I., J.D. Rhoades, and R.J. Prather. 1980. Effect o f exchangeable sodium
percentage, cation exchange capacity, and soil solution concentration on soil
electrical conductivity. Soil Sci. Soc. Am. J. 44:469-473.
Slavich, P.G., and G.H. Petterson. 1990. Estimating solution extract salinity from soil
paste electrical conductivity. An evaluation o f procedures. Aust. J. Soil Res.
28:517-522.
Tanji, K.K., and J.W. Biggar. 1972. Specific conductance models for natural waters and
. . soil solutions o f limited salinity levels. Water Resour. Res. 8:154-153.
Topp, G.C., J.L. Davis, and A.P. Annan. 1980. Electromagnetic determination o f soil
water content: measurements in coaxial transmission lines. Water Resour. Res.
16:574-582.
12
Topp, G.C., M. Yanuka, W.D. Zebchuk, and S. Zegelin. 1988. Determination of
electrical conductivity using time domain reflectometry: soil and water
' experiments in coaxial lines. Water Resour. Res. 24:945-952.
United States Salinity Laboratory Staff. 1954. Diagnosis o f saline and alkali soils.
USDA-ARS Agric. Handb. 60. U.S. Gov. Print Office, Washington, DC.
Vanclooster, M., C. Gonzalez, J. Vanderborght, D. Mallants, and J. Diels. 1994. An
indirect calibration procedure for using TDR in solute transport studies, p. 215-226.
In Time domain reflectometry in environmental, infrastructure and mining
applications. Proc. Workshop, Evanston, IL. Sept. 7-9. 1994. Publ. SP 19-94. U.S.
Dept, o f Interior, Bureau o f Mines, Washington DC.
Vogeler, I., B.E. Clothier, and S.R. Green. 1997. TDR estimation o f the resident
concentration o f electrolyte in the soil solution. A u st J. Soil Res. 35:5515-526.
Ward, A.L., R.G. Kachanoski, and D.E. Elrick. 1994. Laboratory measurements of
solute transport using time domain reflectometry. Soil Sci. Soc. Am. J. 58:10311039.
Zegelin, S. J., I. White, and G.F. Russell. 1992. A critique o f the time domain
reflectometry technique for determining field soil-water content, p. 187-208. In G.C.
Topp, W.D. Reynolds, and R E . Green (ed.) Advances in measurement o f soil
physical properties: Bringing theory into practice. SSSA Spec. Publ. 30. ASA,
CSSA, and SSS A, Madison, WL
13
CHAPTER 2
APPLICATION OF TWO CONDUCTOR-BASED MODELS FOR
SOIL SOLUTION ELECTRICAL CONDUCTIVITY
Introduction
Soil monitoring o f common ionic solutes such as fertilizer salts has become an
increasingly important issue as dictated by environmental and economic concern.
Accurate information regarding soil water status and field solute distributions is needed
so land managers can make informed decisions about quantity and timing o f irrigation
waters and applied chemicals. An increasing number o f studies during the past few years
have investigated use o f time domain reflectometry (TDR) to estimate ionic solute status
o f soils, in the laboratory or field. TDR measures volumetric soil water content (0) (Topp
etal., 1980) and bulk soil electrical conductivity (a a) (Dalton et al., 1984) accurately and
rapidly, using the same probes.
Ionic solute concentration is directly related to the electrical conductivity o f the soil
solution (ctw). Aqueous soil extracts are a well accepted means o f determining ctw,
although many difficulties involved in collecting extracts with conventional techniques
have been identified (e.g., van der Ploeg and Beese, 1977; Lord and Shepherd, 1993).
Direct soil sampling also provides a viable means o f obtaining solution extract; however,
the destructive nature (in particular) and cost considerations again make this an
14
unattractive technique for many applications. Because crw is a more useful index o f solute
concentration than is a a (which is directly measured by TDR), a considerable amount o f
attention has been devoted to characterizing the complex relationships between a a, 0, and
Cw
t in soil-water systems (e.g., Rhoades et al., 1976; Shainberg et aL, 1980; Nadler and
Frenkel, 1980; Bohn et al., 1982; Rhoades et al., 1989; Mualem and Friedman, 1991). To
facilitate research and management applications, it is desirable to employ relationships
that are based on easily measurable (or easily calibrated) properties.
Rhoades et al. (1976) developed a simple conceptual model with empirical
coefficients (designated R76) describing the dependence of cya on two soil conductors
acting in parallel. A bulk liquid phase conductance element (itself dependent upon 0) and
a surface conductance ( a s) component are considered in this model. Following the
approach o f Sauer et al. (1955), Rhoades et al. (1989) later incorporated a third parallel
electrical conducting pathway accounting for the interaction between liquid and solid
phases in series' into a modified version o f the R76 model. This model is designated R89.
Previous studies (e.g., Risler et al., 1996; Mallants et al., 1996; Persson, 1997) have
investigated the R76 and/or R89 model(s) combined with various calibration techniques.
The present study provides an assessment o f these two models under a more diverse set o f
experimental conditions than has been previously reported. The objective o f this study
was to evaluate the abilities o f the R76 and R89 models to estimate ctw based on TDR 0
and Ga measurements under conditions o f concurrent variable soil wetness and ionic
concentrations. In addition, some practical and conceptual issues associated with the
models were explored, including ease o f parameter determination, non-unique sets of
15
calibrated model parameters, applicability o f parameters derived under one type o f
experimental condition to estimate <tw under a separate set o f conditions, and whether a
particular model may be better suited for certain soil conditions. Two types o f laboratory
column experiments were undertaken on repacked and intact soils: a static matrix-type
factorial (multiple combinations o f 0 and Cw
t), and miscible displacement o f solutes under
steady and transient flow conditions. From these experiments, four different methods
were used to determine R76 and R89 model parameters. Results obtained using different
combinations o f calibration models and parameter estimation methods were compared
with independent measurements o f a w from soil solution extracts and column effluent
fractions.
Materials and Methods
Two-Conductors Calibration Models
Soil bulk electrical conductivity (a a) is influenced by three primary factors:
conductance arising from ions in the bulk soil solution (ctw); surface conductance (crs)
primarily due to ions adsorbed on clay minerals; and tortuosity o f the electrical flow path
through the soil matrix (Rhoades et al., 1976). The R76 model is a simple two■conductors approach whereby the liquid and solid phases in the bulk soil are treated as
two macroscopic and parallel conductors contributing to a a:
Ca =OwGT(G)+c ,.
where T(G) is interpreted as a soil-specific transmission coefficient accounting for
[1]
16
changes in the tortuosity o f electrical current flow caused by changes in soil wetness. The
transmission coefficient has traditionally been characterized as a linear function o f 0
(Rhoades et al., 1976):
T(0) = a0 + b
[2]
with empirical soil-specific constants a and b.
Nadler and Frenkel (1980) and Shainberg et al. (1980) found that the Ga-CTw
relationship may become curvilinear at ctw < ~3.5 dS m"1. Rhoades et al. (1989) reported
that this nonlinearity was not significant at Cw
t values > ~ 1.0 dS m '1. Equation [1] is
unable to describe this nonlinearity, and this was addressed by Rhoades et al. (1989). In
the R89 model, a continuous solid pathway is neglected based on its relative lack o f
contribution to the overall cra (Rhoades et al., 1989), resulting in the following two
parallel conductors formula:
( 9 s s + Q 2 g ws<
<?a = .
+ QwocfW
C
[3];
8 ,s O w s + 6 w X
where Cw
ts and ctwc are the soil solution electrical conductivities o f the solid/liquid seriescoupled pathway (‘micropores’) and the continuous liquid pathway (‘macropores’), and
0WS and 0WCare the corresponding volumetric soil water contents. The conductance o f the
soil particles in the series-coupled pathway is denoted ct/ . Similar to T(0) in the R76
model, Rhoades et al. (1989) described Ows as a linear function of 0:
Qws = a 6 + P
with 0WC= 0 - 0WS. The volumetric soil solid content in the solid/liquid series-coupled
[4]
17
pathway, Qss, is determined as:
.
6 , =PbZPs
[5]
with pb and ps the densities o f the bulk soil and the solid particles. The assumption a w =
Cfws = Cfwc is required in order to solve Eq. [3] for crw. This assumption may be valid only
under conditions o f diffusional equilibrium, which is not expected during many solute
breakthrough experiments (Kim et a l, 1998).
Determination o f Model Coefficients
Four methods were used to obtain the coefficients for the two models (R76, R89)
evaluated in this study. M ethod I is a salinity and wetness factorial matrix approach and
has been used previously (e.g. Rhoades et al., 1976; Bohn et al., 1982; Nadler, 1982;
W ard et al., 1994; Mallants et al., 1996; Vogeler et al., 1996; Persson, 1997). This
procedure allows direct determination of the Q-Oa-Gw relationship by generating a family
o f o w vs. o a curves at different levels of 0. Generally the relationship is determined by
adding different amounts o f solutions having variable ionic strengths to discrete soil
columns. This produces a range in both o and 0. After an appropriate equilibration
period, o a and 0 o f each sample are measured (or assumed). The measured 0 and o a can
then be used to calibrate various models to estimate o wfor these soils. In some previous
studies that used this method (e.g., Rhoades et al., 1976; Mallants et al., 1996; Persson,
1997) an assumption was made that o w o f the soil columns was equal to o o f the solution
added to the soils. For this study, o w was measured from soil solution extracts for each
column, similar to the method o f Nadler (1982), Dalton et al. (1984), and Vogeler et al.
18
(1996).
Method 2 combines TDR measurements o f 0 and cra with gw determined from
sampling techniques such as porous solution samplers, soil cores, or soil column effluent
fractions. This type o f calibration approach has previously been used in laboratory soil
column experiments under steady (e.g., Kachanoski et al., 1992; Risler et al., 1996) and
transient water flow (Risler et al., 1996; Persson and Bemdtsson, 1998), as well as for
field conditions (Noborio et al., 1994; Heimovaara et al., 1995; Wraith and Das, 1998;
Nissen et al., 1998; Das et al., 1999). Method I and Method 2 are similar in that TDR
measurements o f 0 and G a are combined with independently measured Gw to determine
(optimize) model parameters. However, Method I uses discrete aa-0 samples, while
Method 2 covers a ‘continuous’ (at least potentially) range in one or both o f these
attributes at the same probe location.
The third parameterization method is based on mass conservation o f an applied
solute pulse having duration to and electrical conductivity
gq .
Total mass density of
laboratory or field solute BTGs [i.e., 2 (Gwt)] are equated to the total mass o f the applied
pulse (Goto). This type o f procedure was .performed by Ward et al. (1994) and Mallants et
al. (1996) where TDR measured Ga and 0 were paired with values o f resident solute
concentration (Cr) to obtain a 0-Ga-Crrelationship for a particular solute. In the approach
o f Ward et al. (1994) and Mallants et al. (1996), Cr was determined from a solute-specific
calibration that requires conditions o f constant 0. In this study we used a procedure
similar to that o f Das et al. (1999) where constant 0 is unnecessary. TDR-measured Ga
19
and 0 were used in the two calibration models and the model parameters optimized byequating mass recovery calculated from predicted (model) ctwto that from ctwmeasured
from effluent fractions.
Method 4 requires conditions o f constant a w. If a sufficient quantity o f ionic
solution is leached through a soil,
cjw will
eventually become constant once the solutes
have been distributed uniformly. After steady ctw is achieved, simultaneous TDR
measurements o f a a and 0 under variable wetness allows determination o f the G-Ga-Ow
relationship. This approach was used by Risler et al. (1996), Persson (1997), and Das et
al. (1999). A benefit o f this approach is that no independent paired measurements of o w
are required. The four methods to determine soil-specific model parameters are
summarized in Table I .
Table I. Calibration methods used for determination o f R76 and R89 model coefficients.
Method
Description
1
Factorial soil column matrix (discrete o w-6 combinations)
2
Optimize TDR 0 and aato independently measured Gw
3
Mass conservation of solute pulse
4
Constant Gw, continuously variable 0 and Ga during soil wetting and drying
Laboratory Calibration Experiments
All 0 determinations were made using the Topp et al. (1980) TDR calibration
equation, which had been previously confirmed for the two soils used. T D R .
measurements o f Ga were based on the Giese and Tiemann (1975) relationship using:
Ga
Z0 ■
IZOteLZ l
[6]
20
where the probe impedance (Z q, O) was determined by immersion in deionized water
(Heimovaara, 1992; Baker and Spaans, 1993), L is probe length (m), and Z l is the
measured resistive impedance load (Q) across the TDR probe.
Soil Column Matrix. Column matrix calibration experiments were carried out in
polyvinyl chloride (PVC) tubing sealed at one end with acrylic discs. A a a-6-aw
relationship was determined for three soils: a repacked Flathead sandy loam (coarseloamy, mixed Pachic Udic Haploboroll) obtained at the Northwest Agricultural Research
Center near Creston, MT; and repacked and intact Amsterdam silty clay loam soils (finesilty, mixed Typic Haploboroll) taken from the Arthur H. Post Experimental Station near
Bozeman, M T (Table 2). All soil materials were collected from the surface (Ap)
horizons.
Table 2. Primary particle size fractions for Flathead SL and Amsterdam SiCL soils.
Size fraction
Flathead sandy loam
Amsterdam silty clay loam
Sand (%)
75
11
Silt(% )
18
60
Clay(%)
7
29
Repacked soils were dried and sieved through 2 mm mesh screen and packed to a
height o f 0.20 m in PVC columns having 0.05 m diameter and 0.23 m height. Packing
was accomplished in two steps: after columns were packed to 0.10 m depth, one-half the
solution was added; once the solution had imbibed, the remainder o f the soils then
solution were added. All repacked columns were packed to a bulk density o f 1.25 Mg
m"3. After all the soil and solution had been added, the columns were sealed at the top
21
with two layers o f parafllm, laid on their sides, and allowed to equilibrate for 30
(Flathead) or 60 d (Amsterdam). All columns were rotated regularly to facilitate uniform
dispersion o f solution within the soils.
Intact 0.20 m length Amsterdam soil cores were collected in 0.23 m length by 0.04
m diameter PVC tubing using a hydraulic core sampler. Based on additional replicate
samples collected at the same time, cores had mean 0 o f 0.26 m3m"3 (SEM = 0.0037) and
mean pb o f 1.37 Mg m"3 (SEM = 0.075). After oven drying at 550C for 10 d, the intact
cores had mean 0 o f 0.12 m3m"3 (SEM = 0.0034). Solution was added to the top surface
o f the cores, and in addition, small holes were drilled in the side o f the columns at 0.07
and 0.14 m from the bottom to facilitate addition and redistribution o f the remainder of
the solution. Parafilm was again placed over the top o f the columns and silicone sealant
was applied to the small holes. As with the repacked Amsterdam columns, the intact
cores were allowed to equilibrate for 60 d. There were a total o f 40 columns for each o f
the Amsterdam soils: five different concentrations o f KCl solution (0, 0.27,1.08, 4.06,
and 7.62 dS m '1), four target 0 levels (0.20, 0.30, 0.40, 0.50 m3 m"3), and two replicates
for each ct-O combination. The Flathead soil column matrix comprised four
concentrations o f KCl solution (0.25,1.0, 3.6, and 7.2 dS m"1), three target 0 levels (0.22,
0.32, 0.42 m 3 m"3), and two replicates o f each <r-0 combination for a total o f 24 columns.
A second soil column matrix experiment was subsequently undertaken using repacked
Flathead soil. Five KCl concentrations were used (0, 0.25, 1.0, 3.6, and 7.2 dS m '1) along
with three target 0 levels (0.10, 0.20, 0.30 m3 m"3) resulting in a total o f thirty columns.
After the equilibration period (30 or 60 d), a three-rod TDR probe (0.198 m rod
22
length, 1.5 m m rod diameter, 10 mm rod spacing) was used to measure 9 and o a in each
column. We used a TDR cable tester (1502C, Tektronix, Beaverton, OR) and a computer
which controlled the cable tester through serial interface. Five different waveforms
obtained from the same embedded probe were analyzed using a program modified from
Spaans and Baker (1993) to ascertain 9 and a a. Means o f the five measured values were
used in the a a-9-aw calibration relationship; measurement standard errors for each column
were exceedingly small. After the TDR analysis was completed, the contents o f the
columns were carefully removed onto a tray where the cores were sectioned into top and
bottom halves. One lateral h alf o f each (top, bottom) sample was allotted for mass water
content (9m) measurement by oven drying, and the other was used for soil solution
extraction. Soil solution extract was obtained by first adding sufficient distilled deionized
(DI) water to the sample to obtain approximately 1:1 [kg:kg] soil-water ratio, followed by
45 minutes o f shaking (Eberbach Corp., Ann Arbor, MI) and 20 minutes o f centrifugation
(RC-5B, Du Pont Company, Newtown, CT) at 19,000 rpm. Centrifuged samples were
decanted and the conductivity o f the extracted solution (a e) determined using a
conductivity meter (Accumet Model 50, Denver Instrument Co., Arvada, CO with Model
3403 electrode, YSI Inc., Yellow Springs, OH). A circulating water bath (RTE-220D,
Neslab Instruments Inc., Newington, NH) maintained the extracted samples at 25°C prior
to analysis. The gravimetric (9m) core sample halves along with known mass of DI water
added allowed calculation o f a dilution factor which was then multiplied by a e to give ctw
at initial sample wetness. The calculated Gw representing the top and bottom o f each
column were averaged, then combined with corresponding TDR-measured Ga and 9 to
23
complete the a a-0-aw suite.
The following relationships were used to determine best-fit model parameters from
nonlinear least squares regression (Wraith and Or, 1998) against measured crw. For the
R76 model, combining [1] and [2]:
O a-O ,
(a6 + b)6
[7]
for the R89 model:
oW
- b ± Vb2 - 4 a c
"
2a
[8]
where a = -(0Ss)(0 - 0Ws), b = [(OssCTa) - (0SS+ 0ws)2(cts') - (0 - 0ws)(0wsCTs' )], and C=
(Ows(Ts7Ca) (Rhoades et ah, 1989).
Steady Flow Experiments. A peristaltic pump (Wiz, Isco Inc., Lincoln, NE) was
used to deliver eluent to the top o f soil columns at a constant rate. Columns were initially
conditioned with a weak KCl solution. Once a constant background concentration (c w)
was reached, based on electrode analyses o f the column effluent, eluent was switched to a
higher KCl pulse concentration (Table 3). Effluent collection was accomplished using a
setup similar to that o f Langner et al. (1998). In this system, advancement o f tubes in the
fraction collector (Retriever, Isco Inc., Lincoln, NE) causes 2 three-way solenoid valves
(at top and bottom o f an intermediary effluent collector) to switch to a sampling position
for approximately IO s allowing effluent to drain into a test tube in the fraction collector.
The valves are then returned to the closed sample accumulation position. Unsaturated
conditions were maintained by supplying negative pressure to the column outlet. A
24
vacuum line was connected to a regulator (Model 44-20, Moore Products Co., Spring
House, PA) and the top solenoid valve, while the bottom solenoid valve was connected to
the column outlet by polyurethane tubing. Columns were affixed to a vacuum chamber
apparatus (Soil Measurement Systems, Tucson, AZ) and suction at the column outlet was
maintained at -20 kPa throughout all column flow experiments, with the exception o f the
10 s sampling periods when position o f the solenoid valves were switched to allow
sample drainage. Soil columns were wrapped with polyurethane tubing and maintained at
25°C by circulating water through the tubing.
Table 3. Selected flow and salinity attributes for steady flow soil column experiments.
Pulse
Application Pore Water
Input Solution a
Velocity
Duration
Rate
Background
Pulse
--------- dSm "1
- pore volumes
cm3 h' 1
cmh "1
Amsterdam Repacked
0.5
4.0
1.1
15
0 .2
Flathead Repacked
0.1
1.7
1.3
80
1.2
Flathead Intact
0.5
4.0
1.2
40
0 .6
Components o f the TDR system were the same as described for the column matrix
experiments, except that WinTDR98 software (Utah State Univ. (1998). Logan, UT.
Revision available: http://psb.usu.edu/wintdr99/) was used for TDR control, acquisition,
and analyses. The basic 0 and a a relationships were the same as for the program modified
from Spaans and Baker (1993). Electrical conductivity o f effluent samples was measured
using the conductivity meter while 0 and CaWere continuously monitored (30-min
interval) using automated TDR. Model parameters were again determined from
optimization against c w measured in effluent fractions, allowing for calculation o f model
25
predicted ctw using Eq. [7] and [8].
Transient Flow Experiments. The experimental setup was similar to that given for
the steady flow columns with the exception o f eluent application. Eluent was applied via
a precision low-flow syringe pump (Soil Measurement Systems, Tucson, AZ) controlled
by a datalogger (2IX , Campbell Scientific, Logan, UT). Some o f the transient flow
experimental conditions are shown in Table 4. Solution was applied at 15 min intervals
for 24 h, followed by 48 h were no application took place. During the first 24 h o f the
cycle, increasing amounts o f solution were applied every 15 min until the 12th h,
followed by 12 h o f decreasing solution application. This resulted in a quasi-sinusoidal
Table 4. Selected flow and salinity attributes for transient wetness soil column
experiments.______________________ ___________________________________
Application
Soil Water Contentf
Solution a
Background
Pulse
RateJ
Min.
Max.
A c? m
m -i
Qo
Amsterdam Repacked
0.5
m 3 I1-T3
111 111
1.9
0.21
n
fCt m
n3 V 1
0.38
5.2
0.34
4.6
Flathead Intact
0.5
4.0
0.27
f measured at TDR probe location
J mean rate based on effluent fractions collected during several wetting and drying cycles
pattern o f wetting and drying similar to that described in Risler et al. (1996). The 48 h
no-addition interval facilitated soil column drainage, resulting in a wider range in 0.
Effluent samples were collected in a fraction collector and analyzed using the same
procedure described for steady flow conditions. Parameters for all models were
determined as previously described with the exception o f calibration Method 4 (where a w
is held constant under variable 0 and hence a a). Several wetting and drying cycles were
26
applied to produce constant crw prior to the pulse application. Once steady crw was
achieved, based on measured column effluent samples, concurrent TDR measurements o f
CJa and
0 were made while 0 continued to vary. This allowed (Method 4) determination o f
model parameters from optimization o f predicted vs. measured a a using Eq. [1] and [3].
Results and Discussion
Results from both repacked Flathead soil factorial matrix experiments were
combined and are discussed in aggregate. Findings from all our column matrix
calibrations are similar to those reported in Nadler (1982) who observed an increase in <jw
measured from solution extracts compared to ctw o f the input solution. Conversely,
Vogeler et al. (1996) noted a 63 to 82% decrease in <jw measured from solution extracts
relative to
cjw
o f the input KCl solutions. Possible explanations given by Vogeler et al.
(1996) were cation exchange (replacement o f Ca2+ by K+), Cl" adsorption, and changes in
the diffuse double-layer. The SiL soil used by Vogeler et el. (1996) was high in organic
matter and contained a high proportion o f volcanic ash which is reflected in low Pb of
0.84 Mg m"3. For the Flathead SL and Amsterdam SiCL soils, values 1.25 to 40, and L I
to 18 times higher respectively were measured for <tw compared to cr o f the added KCl
solutions. Similar to the trend observed in Nadler (1982), the magnitude o f the
differences decreased with increased soil 0. Part o f the discrepancy between or o f the
input solutions and extracts is probably due to concentration o f salts resulting from oven
drying the soils during their initial processing. After the soils were re-wetted, the salts
27
left behind during oven drying would then be available to augment the a attributed to the
input solution. Based on a subsequent experiment using the Amsterdam soil where we
compared oven dried vs. ambient wetness initial soil conditions, we did confirm this
phenomenon, though it was relatively insubstantial in comparison to the differences noted
above. In addition, we assumed a linear relationship between 0 and a w from our
dilutions. This may be a precarious assumption (e.g. Reitemeier, 1946; Nadler 1997) as
the general tendency of dilution is to increase total dissolved ions (e.g. Khasawneh and
Adams, 1967; Ulrich and Khanna, 1972; Fotovat et al., 1997). A number o f potential
mechanisms that could explain an increase in the total amount o f electrolytes upon
dilution are described in Fotovat et al. (1997) and include: cation desorption from
exchange sites; dissolution o f sparingly soluble salts; hydrolysis o f exchangeable cations;
and a double-layer effect. Experimental evidence is not conclusive according to
Reitemeier (1946), who indicated that several studies reported that total ions dissolved in
solution remained constant upon dilution for a wide range in 0. Unfortunately our
experiments were not designed to discern the effect o f dilution on total dissolved ions;
therefore, without further intensive experimentation it is uncertain whether the o a-0-aw
relationships we established based on our soil matrix experiments and experimental
techniques might be substantially different were a different method used to obtain ctw.
Unlike the approach o f Mallants et al. (1996) who fitted a different value o f crs
(R76) for each 0 series, a single soil-specific value o f cts (Table 5) was determined from
each factorial matrix calibration experiment. It is apparent (Figs. I, 2) that the approach
o f Mallants et al. (1996) would have resulted in better R76 model fits for each separate 0
28
series. However, our results indicated that singular values for a, b, and a s adequately
described the CTa-0-aw relationship over a wide range in 0 (Table 5). This is in conceptual
agreement with the model itself, and avoids the necessity to interpolate between discrete
sets o f model coefficients as soil wetness changes. Inclusion o f a a and gw measurements
from the lowest 0 series for each column matrix experiment did not allow a reasonable fit
to the R76 model (r2 < 0.60 for all soils), so these were not used. However, data
generated from the Flathead and Amsterdam low 0 series are in accordance with Mallants
et al. (1996) (reported by Nadler, 1998) who for a similar calibration study using a sandy
loam soil extrapolated a value o f Cst= 0.04 dS m"1 for a low (0.12) 0 series.
Table 5. Best fit parameters for factorial soil column matrix experiments using R76 and R89
models for soil solution electrical conductivity in Flathead SL and Amsterdam SiCL soils.
Flathead
Amsterdam
Repacked
Repacked
Intact
R76 Modelt
a
1.27
1.95
1.95
b
0.006
-0.18
-0 .2 2
CTs
0.021
0.48
0.50
r2
0.95
0.91
0.87
R89 Modelt
a
0.45
0.11
-0.16$
P
0.050
0.14
0.25$
CTs'
r2
0.019
0.62
0.63
0.95
0.93
0.90
t lowest 0 series not used in determination of model parameters
J optimized values do not result in physically realistic 0WSin the context of R89 model
29
Because cya is affected by the tortuosity o f electrical flow paths through the soil
matrix, T(G) is presumably an indicator o f soil structural development and resultant pore
size distribution. Contrary to our expectations, nearly identical model coefficients were
determined for the repacked and intact Amsterdam soils (Table 5). The intact cores were
taken from an agricultural field, and therefore it is possible that there were no substantial
differences in pore size distribution between the intact and repacked soils as a result of
annual tillage operations. However, Nadler (1991) reported similar results for four soil
types and attributed similar a a-a w relationships for disturbed and undisturbed soils to
recovery o f the macroaggregate structure upon wetting and drying. Microaggregate
structure was assumed to have not changed upon disturbance to the soil (Nadler, 1991).
Equation [8] (R89) described the measured column matrix
Cra-G -C rw
relationship
similarly to Eq. [7] (R76). As with the R76 model, inclusion o f measurements from the
lowest Q series for each matrix experiment precluded a reasonable fit to the model, thus,
they were not used in the fitting procedures. Rhoades et al. (1989) indicated that model
parameters a and |3 (used to describe the dependence o f Gws on 6) were essentially
independent o f soil type and reported values o f a = 0.468 and (3 = 0.064 from laboratory
measurements on field soil cores, and a = 0.639 and (3 = 0.011 from in situ field
determinations. Best fit a and (3 values (Table 5) for the Flathead SE were more similar
to those reported by Rhoades et al. (1989) than were those for Amsterdam SiCL repacked
and intact soils. This difference is not entirely unexpected. Up to a certain threshold 6
value, only pores sizes corresponding to Gws (‘micropores’) contain soil solution. Above
30
Mean 0
0 0 .1 0
A0.14
+ 0.16
♦ 0.25
X 0.29
■ 0.37
Figure 1. Measured results for repacked Flathead soil column matrix calibration experiment.
Linear fit for each 0 series shown for illustrative purposes only, as a single value of R76 and
R89 model parameters were determined for the entire data set.
Mean 0
0 0 .1 4
A 0.24
+ 0.34
♦ 0.44
Figure 2. Measured results for repacked Amsterdam soil column matrix calibration experiment.
Linear fit for each 0 series shown for illustrative purposes only, as a single value of R76 and
R89 model parameters were determined for the entire data set.
31
this level, pores corresponding to 0WC(‘macropores’) begin to fill and their volume
increases linearly as 0 increases (Rhoades et al., 1989). According to our fitted results,
threshold values o f 0 where this transition occurred were 0.09 (Flathead repacked) and
0.15 m 3m "3 (Amsterdam repacked). This is in relative accordance with expectations
based on textural differences (Table 2). The finer Amsterdam SiCL soil likely has a
higher proportion o f ‘micropores’ relative to the Flathead SL soil. Below each soil’s
threshold 0 value (i.e. the point where Ows = 0) the model is incapable o f describing the
CTa-O-CTw relationship. W hen this occurs, the value o f 0WSbecomes greater than 0 which is
physically impossible. It could be logically assumed that 0 = Ows in this range; however,
doing so renders the model unusable as the denominator in [8] goes to zero. Attempts to
apply calibration data having 0 < Owc thus result in poor optimization outcomes.
A negative value for the intact Amsterdam soil R89 parameter a (e.g.. Table 5)
indicates a decrease in Ows with increasing 0. This is both physically unrealistic (in the
context o f the conceptual model) and contrary to results o f Rhoades (1989), who reported
that both Owc and Ows increased with increasing 0. However, if optimized a and (3
parameters determined from the repacked Amsterdam soil (which are consistent with the
pattern expressed by Rhoades (1989)) are applied to the intact Amsterdam soil core data,
the goodness o f fit between measured and predicted ctw decreases only insignificantly
from r 2 o f 0.87 to 0.86. This is a potential indication o f obtaining non-unique best-fit
model coefficients, as will be addressed below.
Mallants et al. (1996) and Persson (1997) found poor agreement between R76
32
model predictions from soil column matrix experiments as applied to steady and transient
flow experiments respectively. Application o f model (R76, R89) parameters determined
from our factorial matrix experiments to TDR measurements o f CTa and 6 from flow
experiments (and vice versa) also resulted in poor agreement with measured effluent ctw
(r2 < 0.50 in all cases). There are a number o f potential reasons for the disparity: matrix
experimental technique may have led to an anomalous C3
t-O-Ct w relationship as mentioned
previously; inability o f the model(s) to accurately describe the C3
t-O-Ct w relationship under
certain experimental conditions, and; differences could exist in the C3
t-O-Ct wrelationship
determined from TDR measurements in experiments where diffusional equilibrium has or
has not occurred (Kim et al. 1998). The R89 model assumption that CTw= ctwc = ctwswas
discussed previously. In addition, TDR and soil solution extracts measure resident solute
concentrations while effluent fractions are considered to represent flux-averaged
concentrations (Parker and van Genuchten, 1984). Resident and flux-averaged
concentrations are likely to be different unless diffusional equilibrium is reached. This
criteria is not expected to occur during solute breakthrough experiments, especially under
transient wetness.
A timing mismatch between TDR and effluent breakthrough curve (BTC)
measurements resulted from placement o f TDR probes 3.0 to 3.5 cm above the soil
column outlets. To account for the spatial separation o f TDR and effluent measurements,
all effluent-generated ctw BTC s were shifted back in time. For steady flow experiments,
effluent BTCs were shifted by the pore volume fraction within the total soil volume that
was below the TDR probe. Because variable wetness did not allow determination of a
33
unique water-filled pore volume, transient flow BTCs based on effluent fractions were
shifted in time based on visual observation to correspond with TDR BTCs.
Model parameters determined by calibration Methods 2, 3, and 4 for all flow
experiments are summarized in Table 6 . As expected, all calibration experiments showed
Cs (R76) and crs' (RB9) were much higher for the SiCL than for the SL soil, presumably
due to differences in clay content (Table 2) and perhaps clay mineralogy (which was not
investigated). Neither set o f optimized model parameters for the intact Flathead soil
(steady flow) is physically/conceptually realistic within the constraints o f the R76 and
R89 models, yet both provide excellent agreement with measured effluent ctw. In fact, a
number o f model parameter combinations provided equally good fit (r2 as criterion) to
measured <yw, a possible result o f the rather small variation in 0 for this soil. For
example, values o f a = 1.95, b = 0.050, and as - 0.059 (R76 model) also produce in an r2 '
o f 0.98 when calibrated to the effluent o\v. However, when these two sets o f parameters
are applied to the intact Flathead soil transient flow experiment, the subsequent
agreements with effluent a w are very different (RMSE o f 1.32 dS m "1compared to 0.20
dS m"1). Caution should therefore be exercised if R76 and R89 model coefficients
determined from steady flow experiments are to be used to predict a w under conditions o f
variable wetness.
Similar to steady flow experiments, we also encountered the potential to obtain non­
unique model parameters for calibration Method 4 (Fig. 3). In this case, the problem may
be exacerbated by a lack of variance (range) in ctw rather than 0. While multiple sets of
optimized parameters for the Amsterdam SiCL (e.g. a = 5.43, b =.-0.48, cts = 0.29;
34
B est Fit P aram eters
a = 2 .1 9
b = -0 .1 6
CTs = 0.11
a = 2 .9 9
b = -0 .6 4
Cst = 0 .2 0
r2 = 0 .9 9
r2 = 0 .9 9
Ul SP) eS
O
M easured
Fitted (S et I)
Fitted (S e t II)
6 a w (dS m"1)
O
M easured
------- Predicted (S et I)
- - - - Predicted (S et II)
(,.UI SP) mO
Pore Volumes
Figure 3. Top: Two parameter sets obtained using calibration Method 4 for the intact Flathead
soil with the R76 model. Bottom: Predicted ctwfor the intact Flathead soil (transient flow BTC)
based on the two sets of best fit R76 model parameters in top panel.
Table 6. Best fit R76 and R89 model parameters from soil column flow experiments for Flathead SL and Amsterdam SiCL soils.
Amsterdam SiCL
Flathead SL
Repacked
________________Intact_____________
Steady Flow
Repacked
Steady Flow
______ Transient Flow
Steady Flow
Transient Flow
Calibration Methodt
2
3
2
3
4
2
3
2
3
2
3
4
R76 Model
a
-18.27
1.91
1.52
1.90
2.19
5.64
1.40
-2.54
2.99
4.33
4.40
5.43
b
7.50
-0.02
0.082
-0.03
-0.16
-1.50
-0.02
1.45
-0.035
-0.29
-0.30
-0.48
CTs
0.092
0.11
0.094
0.09
0.11
0.056
0.060
0.37
0.35
0.29
0.29
0.29
r2
0.98
0.96
0.96
0.96
0.99
0.99
0.98
0.97
0.92
0.90
0.89
0.99
R89 Model
a
7.82$
7.82$
-0.007$
-0.007$
-0.21$
-1.56$
-1.56$
1.93$
1.92$
-2.64$
-2.65$
-2.25$
P
-2.80$
-2.80$
0.14$
0.14$
0.19$
0.74$
0.74$
-0.46$
-0.47$
0.66$
0.64$
0.31$
CTs'
0.12
0.12
0.12
0.12
0.11
0.064
0.065
0.63
0.64
0.49
0.50
0.34
r2
0.99
0.99
0.96
0.96
0.99
0.99
0.99
0.97
0.95
0.80
0.78
0.99
t Method 2 involves optimizing parameters based on the goodness of fit with a measured Cw
t BTC (from effluent fractions); Method 3 is a
mass-balance approach where parameters are optimized by equating the mass density of the solute BTCs with model predicted BTCs;
Method 4 requires steady ctwwhile 0 and CTa vary which allows for parameter estimation without independently measured ctwdata.
I values do not result in physically realistic Gws in the context of the R89 model
36
a = 1.50, b = 1.88, crs = 0.0022) produce an r2 o f 0.99 using calibration Method 4, the
RMSE generated from the respective parameter sets when applied to the Amsterdam
SiCL transient GvvBTC more than doubles from 0.16 to 0.33 dS m"1.
We found that some R76 and R89 model parameters had very high degree of crosscorrelation (Table 7), especially between a and b (R76) and a and (3 (R89), which
potentially indicates over-parameterization o f the models, thus increasing the probability
o f obtaining non-unique parameter sets. A single set o f values suggested by Rhoades et
al. (1989) could be used for a and (3 thus reducing the number o f fitted parameters for the
R89 model. However, based on our results and those o f Vanclooster et al. (1994), it
appears more realistic to assume that a and (3 are soil specific. Substitution o f alternative
functional forms for T(0) in R76 and 0WS(0) in R89 may provide more robust (unique)
model parameter sets.
Table 7. Correlation coefficients (r)t for R76 and R89 parameter values reported in
Tables 5 and 6 .
R76 Model
R89 Model
a:b
a:CTs
b:cts
a:(3
OCCTs'
P:cts'
Flathead Repacked (Matrix)
-0.860
0.486
-0.837
-0.729
0.420
0.278
Flathead Intact (Steady Flow)f
-0.999
-0.406
0.396
-0.999
0.452
-0.445
Flathead Intact (Transient Flow){
-0.975
0.168
-0.372
-0.973
0.066
0.152
Amsterdam Repacked (Matrix)
-0.894
0.374
-0.706
-0.922
0.073
0.270
Amsterdam Repacked (Steady Flow)!
-0.991
-0.290
0.170
-0.998
0.286
-0.242
Amsterdam Repacked (Transient Flow)! -0.893
t PROC NUN, SAS Institute Inc. 1991.
J Calibration Method 2 used for flow experiments.
0.514
-0.833
-0.964
-0.626
0.782
37
B est Fit R 76 Param eters
a = 1.52
b = 0 .0 8 2
a , = 0 .0 9 4
O M easured
------ R 76 Fitted
+
r2 = 0.96
R 89 Fitted
X)
B est Fit R 89 Param eters
ifp
a = -0 .0 0 7
Ig g L
b = 0 .1 4
CTs = 0 .1 2
r2 = 0 .9 6
P ore V olum es
Figure 4. Fitted (optimized) ctwfor transient flow BTC using best fit Method 2 parameters from
R76 and R89 models for intact Flathead soil.
O
B est Fit R 76 Param eters
a = 4 .3 3
b = -0 .2 9
M easured
------- R 76 Fitted
------- R 89 Fitted
r2 = 0 .9 0
B est Fit R 89 Param eters
a = -2.64
b = 0 .6 6
r2 = 0 .8 0
P ore V olum es
Figure 5. Fitted (optimized) aw for transient flow BTC using best fit Method 2 parameters from
R76 and R89 models for repacked Amsterdam soil.
38
Results (Table 6) indicate little substantial difference (r2) in the capability o f the two
models to describe the a a- 0-(Tw relationship for the transient flow experiments and any
combination o f calibration methods used in this study, with the exception o f Methods 2 .
and 3 for the Amsterdam soil. Figures 4 and 5 show the best fit o f both calibration
models to transient flow BTCs for both soils. Both sets (Flathead and Amsterdam) o f a
and (3 parameters determined from the R89 model not only differ substantially from those
suggested by Rhoades et al. (1989), but are physically unrealistic according to the model.
Our results along with those o f Kim et al. (1998) indicate that the R89 model may not be
appropriate to use under strongly transient wetness conditions.
equal to
G ws
G wc
may not have been
for our miscible displacement experiments, with the possible exception o f
(partial) periods when there was no solution application. Because o f the greater range in
0 for the Amsterdam soil (Table 4), it is likely that differences between G w c and
G ws
occurred more often than, and were more pronounced than for the Flathead soil. This
may partially explain the poorer fit o f the R89 relative to the R76 model for the
Amsterdam soil.
39
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43
CHAPTER 3
PREDICTING SOIL SOLUTION ELECTRICAL CONDUCTIVITY
UNDER LABORATORY AND FIELD CONDITIONS
Introduction
Maintaining, and in some instances improving soil and water quality is a priority
among land stewards and scientists alike. Soils and water bodies are sinks for many
pollutants including those generated from common agricultural practices. Many solutes
derived from fertilizer salts become potential groundwater contaminants once leached
through the upper soil profile. Aside from environmental concerns, monetary
considerations increasingly advocate efficient use o f soil-applied chemicals. Increasingly
intensive farming practices require land managers to make informed decisions regarding
the quantity and location o f chemical inputs. Rapid and reliable measurement techniques
that are able to assess ionic solute distributions (e.g., fertilizer salts) in soils could provide
farmers with a potentially useful management tool. In addition, ionic contaminant
monitoring and rehabilitation o f contaminated soils could be expedited by such
techniques.
Time domain reflectometry (TDR) is an established method for measuring
volumetric soil water content (0), is robust in terms o f low sensitivity to local soil
conditions, and has high spatial and temporal resolution (Topp et al., 1980; Wraith and
44
Baker, 1991). TDR can also measure bulk electrical conductivity (a a) in the same soil
volume using the same probes (Dalton et al. 1984). Becaiuse o f this unique ability, TDR
has shown promise to monitor ionic solute distributions under transient soil wetness
conditions (Risler et al., 1996; Persson, 1997; Hart and Lowery, 1998; Das et al., 1999).
Resident solute concentrations (Cr) can be estimated from a a measurements by
invoking explicit or implied calibration models. Other available techniques to determine
Cr in situ such as solution samplers and soil cores also have inherent advantages and
limitations but do not have the potential o f TDR to provide fast, real-time estimates. Soil
solution electrical conductivity (ctw) is directly related to Cr and thus is a more useful
index o f soil salinity than is c a. An appreciable effort has already been put forth to
elucidate and model the complex relationships between cra, 6 , and Cw
t in soil-water
systems (e.g., Sauer et al., 1955; Gupta and Hanks, 1972; Rhoades et al., 1976; Shainberg
et al., 1980; Nadler and Frenkel, 1980; Bohn et al., 1982; Rhoades et al., 1989; Mualem ■
and Friedman, 1991). Additional efforts, particularly in field settings, are needed to
investigate the effectiveness o f various models and calibration methods to estimate ctw in
situ.
This combined laboratory and field study was undertaken to help define the utility
o f three physical/conceptual models to predict crw under diverse experimental conditions.
Two categories o f laboratory column experiments were completed using repacked and
intact soils: a static soil matrix factorial (multiple combinations o f 0 and g w); and ionic
solute miscible displacement under steady and transient flow conditions. These
45
experiments were combined w ith four different calibration methods to optimize soilspecific model parameters. Predictions o f <yw obtained using the Mualem and Friedman
(1991) model were compared with independent measurements o f Cw from soil solution
extracts and soil column effluent fractions. The efficacy o f applying model parameters
determined in a laboratory setting to predict Gw under field conditions was then examined.
Best-fit parameters from the MF model, as well as those obtained for the Rhoades et al.
(1976; R76) and Rhoades et al. (1989; R89) models (Chapter 2) were combined with
TDR measurements o f 0 and
Ga
to estimate
g w
in the root zone o f a peppermint {Mentha
piperita L.) field. TD R G w estimates were compared with independently measured G w
from soil core solution extracts obtained concurrently from the same field areas. Some
results from the field study have been reported previously (Das et al., 1999). However,
this paper builds upon the work o f Das et al. (1999) by evaluating an additional model
(R89) and two additional calibration techniques, using new calibration data.
Materials and Methods
Theoretical Background
Many relationships have been proposed between
Ga
and
Gw
in porous media.
M ualem and Friedman (1991) developed one such conceptual model based on assumed
similarity between electrical and water flow lines for a given hydraulic gradient:
Ca = O w (G-Gr)Fg
M
where 0r is residual water content, 0 -0r is the mobile pore water content or effective water .
46
content (0eff), and Fg is a 6 -dependent geometry (flow tortuosity) function. Mualem and
Friedman (1991) proposed Fg as the ratio o f the hydraulic conductivity o f the soil to that
o f a bundle o f straight capillaries having the same effective pore diameter distribution.
Their Fg is commonly expressed as:
[2]
where 0 is relative saturation [(0 - 0r)/(0s - 0r)], 0Sis saturated water content, h(x) is the
soil water retention function subjected to integration and P is an empirical parameter that
can be determined from known <ja and ctwat two or more 0. Combining Eq. [2] with [ 1]
yields
f - i - d x
p+i
a a = a w0 eff
j O h(x)
[3]
■’o h (x )2
Using the van Genuchten (VG) (1980) water retention function Heimovaara et al. (1995)
obtained a closed form solution to Eq. [3]:
Qp+i
CTa - a W^eff
I-(1-0/m)
1_ ( 1 _ © A ) C
[4]
where m = 1- 1/n and q = 1-2/p are empirical parameters describing the shape of h( 0), and
may be estimated using a two step optimization process (Heimovaara et al., 1995). Other
47
water retention models are available and some have been adapted for use with the MF
model (Weerts et al., 1999; Das and Wraith, in review) but were not considered here.
The R76 approach is a simple two-conductors model whereby the liquid and solid
phases in the bulk soil are treated as two parallel conductors contributing to CTa:
Ca = CwT(G) 8 + Cs
[5]
where c s is the electrical conductivity attributed to exchangeable ions along the surfaces
o f soil solids, and T(0) is interpreted as a soil-specific transmission coefficient accounting
for changes in the tortuosity o f electrical current flow caused by changes in soil wetness.
T has traditionally been characterized as a linear function o f 9 (Rhoades et al., 1976):
[6]
T(0) = a0 + b
with empirical soil-specific constants a and b.
Rhoades et al. (1989) developed a more complex conductor-based model (R89), in
part to address the issue o f curvilinearity between <ja and ctw at low ctwas discussed by
Nadler and Frenkel (1980), Shainberg et al. (1980), and others. A continuous solids
conductance pathway is neglected in the R89 model based on its relative lack of
contribution.to the overall CTa (Rhoades et al/, 1989), resulting in the commonly utilized
two parallel conductors formula:
( 8 SS +
G
O
s s CTw s
2 W vsg S
+ 6
w s°
+ 6 WC ^ w c
[7]
s
with Cw
ts and Cw
tc the soil solution electrical conductivities o f the solid/liquid seriescoupled pathway (‘micropores’) and the continuous liquid pathway (‘macropores’), and
48
0WSand 0WCthe corresponding volumetric soil water contents. The surface conductance
element in the solid/liquid series pathway is denoted <ts'. Similar to T(0) in the R76
model, Rhoades et al. (1989) described the magnitude o f 0WS in the solid/liquid series
pathway as a linear function o f 0 :
0ws= a0 + p
[8]
with 0WC= 0 - 0WS.
The Topp et al. (1980) TDR calibration equation, previously confirmed for these
soils, was used to determine 0 under laboratory and field conditions. TDR a a
measurements were based on the Giese and Tiemann (1975) relationship using:
oa = —
a
----
[9]
120tiLZ l
where the probe impedance (Zo, O) was determined by immersion o f probes in deionized
water (Heimovaara, 1992; Baker and Spaans, 1993), L is TDR probe length (m), and Z l is
the measured resistive impedance load (Q) across the embedded probes.
Laboratory Calibration Experiments
The soil water retention relationship [0(h)] required for Fg [2] in the MF model was
determined for two soils: Flathead sandy loam (coarse-loamy, mixed Pachic Udic
Haploboroll) obtained at the Northwest Agricultural Research Center near Creston, MT,
and Amsterdam silty clay loam (fine-silty, mixed Typic Haploboroll) taken from the
Arthur H. Post Experimental Station near Bozeman, MT (Table I). For both Flathead
and Amsterdam soils, 0(h) was obtained with a pressure plate apparatus (Klute, 1986).
49
Data were collected in the range 0 to -80 kPa for the Flathead soil (Das et al., 1999) and 0
to -1300 kPa for the Amsterdam soil. VG model parameters (a, n, m, p, q in Eq. [4])
were determined by fitting to measured water retention data using nonlinear least-squares
optimization (Wraith and Or, 1998). Unlike Heimovaara et al. (1995), we did not fix a at
the value obtained during the first step in the optimization process (m,n) during the
second (p,q) step. Following the approach o f Das et al. (1999), we fit a separately in both
optimization steps, avoiding a mathematical inconsistency inherent in the method used by
Heimovaara et al. (1995).
Table I. Primary particle size fractions for Flathead SL and Amsterdam SiCL soils.
Size fraction
Flathead sandy loam
Amsterdam silty clay loam
Sand (%)
75
11
Silt (%)
18
60
Clay (%)
7 :
29
Two categories o f laboratory soil column experiments were performed and are
described in greater detail in Chapter 2. They included a soil salinity and wetness
factorial matrix (different combinations o f 0 and a w), and ionic solute breakthrough under
steady (Table 2) and transient (Table 3) flow conditions. Analogous to methods reported
in Chapter 2 where laboratory experiments were combined with four different calibration
approaches to provide parameter sets for the R76 and R89 models, we optimized the MF
model (3 parameter using:
50
X
aW
/m
2
[ 1.0]
for the same soils under the same experimental conditions.
Calibration Method I (Table 2) was used in conjunction with the soil matrix
factorial experiments and allowed estimation o f model parameters from measurements o f
discrete ctw-6 samples. Calibration Methods 2 and 3 were used with both transient and
steady flow ionic solute breakthrough experiments. Method 2 is similar to Method I in
Table 2. Calibration methods used for determination o f R76 and R89 model coefficients.
Method
DescriptionI
I
Factorial soil column matrix (discrete ctw-9 combinations)
2
Optimize TDR 0 and CTa to independently measured ctw
3
Mass conservation of solute pulse
4
Constant CTw, continuously variable 0 and CTaduring soil wetting and drying
that model parameters were estimated based on agreement with independently measured
ctw.
However, Method I uses discrete CTw-G samples, while Method 2 covers a
‘continuous’ (at least potentially) range in one or both o f these attributes at the same
probe location. Method 3 is a mass-balance approach where model parameters were
determined (optimized) by equating mass recovery calculated from predicted (model) ctw
to that from ctwmeasured in the column effluent fractions. Method 4 was used only with
the transient flow experiments. Conditions o f constant CTw are necessary for this method
and were accomplished by leaching sufficient solution through the soil column.
I
51
Simultaneous TDR measurements o f variable <Ta and 0 (at constant crw) then allowed for
optimization o f model coefficients (Risler et al., 1996). Further details on the calibration
methods used in this study are presented in Chapter 2.
Field Study
A field experiment was performed from 15 April to 6 August, 1996 at the
Northwest Agricultural Research Center near Creston, MT. This is the same location
(within about 0.25 mi) where the Flathead soil used in the laboratory investigations was
collected. The study area comprised four contiguous 21 x 6 m plots within a field under
peppermint cultivation. An automated TDR system measured 0 and cra every 6 h for three
soil depths (0.15, 0.45, 0.90 m) at three locations within each plot. Thermocouples were
placed near each TDR probe to compensate measured CTa for ambient temperature.
Sprinkler irrigation was applied approximately weekly during the latter half of the
growing season. The study site was fertilized the previous October and on day o f year
(DOY) 99 (9 April). KNO 3 salt was hand-applied to plots I, II, and III at 300,150, and 75
kg N ha ' 1 respectively on DOY 170(19 June). Plot IV served as a control, with no added
KNO 3. Soil core samples were collected every I or 2 weeks at three depth increments
(0.10-0.20, 0.35-0.55, 0.80-1.00 m) at five randomly selected locations within each plot at
each sample date. ctw was measured from solution extracts obtained from each soil core
using the methods outlined in Chapter 2. Additional details regarding experimental
procedures for the field study were reported in Wraith and Das (1998) and Das et al.
(1999).
52
Model parameter estimates obtained for the Flathead SL soil using the MF, R76,
and R89 models and the four calibration methods were applied to TDR measurements o f
field soil 0 and a a to generate TDR a w estimates for comparison with those from soil core
solution extracts. The calibrated R76 and R89 parameters were presented in Chapter 2.
Results and Discussion
Laboratory Calibration o f Model Parameters
Measured soil column flow attributes are summarized in Tables 3 and 4. Best fit
parameters for the VG soil water retention model for both soils are shown in Table 5.
Table 3. Selected flow and salinity attributes for steady flow soil column experiments.
Pulse
Input Solution a
Application Pore Water
Background
Pulse
Duration
Rate
Velocity
--------- dS m '
- pore volumes
cm3 h"1
cm h'1
Amsterdam Repacked
0.5
4.0
1.1
15
0.2
Flathead Repacked
0.1
1.7
1.3
80
1.2
Flathead Intact
0.5
4.0
1.2
40
0.6
Table 4. Selected flow and salinity attributes for transient wetness soil column
experiments.__________________________________________________________
Application
Soil Water Content+
Input Solution a
Background
Pulse
Min.
Max.
RateJ
U O III
Amsterdam Repacked
0.5
-i
cm3 k-1
n
m 3m
m
m-3
1.9
0.21
0.38
5.2
0.34
4.6
0.27
Flathead Intact
0.5
4.0
t measured at TDR probe location
$ mean rate based on effluent fractions collected during several wetting and drying cycles
53
Table 5. Measured van Genuchten (1980) soil water retention parameters for Flathead
and Amsterdam soils, using a two-step optimization process.______________________
------------- Step I ----------------------- Step II ----------Soil Type
Flathead SL
Amsterdam SiCL
t m = I - 1/n
I q = I - 2/p
(%m.n
0.22
n
mt
r2
1.37
0.27
0.092
1.44
0.31
P
2.32
qt
r2
0.96
a p.q
0.33
0.14
0.98
0.98
0.14
2.38
0.16
0.99
MF model prediction agreement with independently measured crw was substantially
better in experiments using the Flathead SL soil relative to those using Amsterdam SiCL
soil. Predictions generated from the transient flow experiment with Amsterdam soil were
especially poor compared to those for the Flathead soil. This may be explained in part by
the greater magnitude in wetting and drying observed for the Amsterdam soil column
relative to that o f the Flathead soil (Table 4). In addition, the disparity in model
performance between the two soils may be related to soil textural (and perhaps
mineralogical) differences. The potential contributions o f surface conductance (a s) to a a
is unaccounted for by the MF model. Nadler (1991) emphasized the relative importance
o f Cst by reporting that it can comprise a substantial proportion o f CTa depending on 0,
mineralogy, and the concentration of ions in solution. Ions residing on the surfaces of
clay minerals constitute the major contributions to cts (Nadler and Frenkel, 1980).
Considering that the Flathead soil is low in clay (Table I), cts would not be expected to
contribute appreciably to CTa for this soil relative to the Amsterdam soil which has about
29% clay fraction. Results presented here and statements made elsewhere (Mualem and
Friedman, 1991; Vanclooster et al„ 1994) suggest that the utility o f the MF model may be
54
limited primarily to coarse-textured soils.
Substantial variation in the value o f optimized P for both soils from different
experiments and calibration approaches was observed (Table 6). Analogous results were
also reported in Chapter 2, where dissimilar parameters were obtained using the R76 and
R89 models under the same experimental conditions as applied to MF here, p ranged
from -1.139 for the Amsterdam SiCL transient flow experiment (Method 4) to 0.396 for
the Flathead SL soil matrix experiment (Method I). Other studies (Heimovaara et al.,
1995; Leij et al., 1997; Das and Wraith, in review) have also obtained similar values for
Table 6, Best fit MF model parameter P for all experiments and calibration approaches.
Experiment /
Flathead SL
Amsterdam SiCL
Calibration Approach
Repacked
Intact
Repacked
Pfr2)
-0.526 (0.65)
Soil Matrix / Method I
0.396 (0.94)
-
Steady Flow / Method 2
0.053 (0.91)
-0.134 (0.97)
-0.907 (0.75)
Steady Flow / Method 3
-0.089 (0.88)
-0.197 (0.97)
-0.957(0.71)
Transient Flow / Method 2
-
-0.112(0.92)
-1.030(0.26)
Transient Flow / Method 3
-
-0.125 (0.92)
-1.052(0.24)
Transient Flow / Method 4
-
-0.246 (0.99)
-1.139(0.62)
Intact
-0.575 (0.58)
fitted p. Predicted ctw for solute breakthrough curves (BTCs) under transient flow
conditions using the MF model with different calibrated estimates o f p provided
inconsistent agreement with <twmeasured in the column effluent (Fig. I, 2). The curves
based on P derived from the soil matrix experiments substantially overpredicted effluent
a w for both soils. This may be a result o f dissimilar techniques used to measure ctw
(0
T
$
b
1.0
P o re V o lu m es
Fig. 1 Predicted ctw for the intact Flathead SL soil using the MF model with best fit parameters obtained from 5 different experiments.
Measured data is from transient flow miscible displacement experiment.
4 .5
O
M easured (effluent fractions)
------------Transient Flow / Method 2 (repacked)
---------- Soil Matrix / Method 1 (repacked)
S tead y Flow / Method 2 (repacked)
Transient Flow / Method 4 (repacked)
3 .5 -
"T l
,y
;-v ^ ,
E
(/>
T
5
2 .5 -
S
vv^_y
I
\
Z1
U
W
V
b
0 .5 4------------------------------- 1------------------------------- 1
0 .0
0 .5
1 .0
1 .5
2 .0
2 .5
P o re V o lu m es
Fig. 2 Predicted
ctw for
the repacked Amsterdam SiCL soil using the MF model with best fit parameters obtained from 4 different
experiments. Measured data is from transient flow miscible displacement experiment.
3 .0
57
among the flow column and soil column matrix experiments (Chapter 2). Nadler (1997)
pointed out that for most soils it may be unrealistic to assume cyw can be reconstructed
from aqueous extract salinity (a e) by considering dilution only. However, an exact
relationship between c w and a e for a particular soil would be difficult and timeconsuming to quantify.
Prediction o f the intact Flathead soil transient BTC based on P optimized from the
repacked Flathead soil steady flow experiment mimicked the measured BTC in shape but
systematically overestimated its magnitude (Fig. I). For the same soils and experimental
conditions, we found the same results with the R76 and R89 models (Chapter 2). This is
likely a result o f dissimilar experimental conditions that the two soil columns (repacked,
intact) were subjected to (Table 2). Because P estimated using Method 2 from steady
flow and transient flow experiments for the intact Flathead soil were similar (Table 6),
these produced nearly identical predictions for the measured transient flow BTC (Fig. I).
Note that the transient flow P was optimized to measured effluent G w shown in Fig. I,
while P from the steady flow experiment was obtained from the same column but a
different set o f experimental conditions. For the same two experiments (Method 2,
steady and transient flow) but with the Amsterdam soil, there was more variation in
1
estimated P (Table 6) which is visually apparent from the model predictions generated
from these parameters (Fig. 2). We found that for the transient wetness experiments, P
estimated from calibration Method 4 (sequential wetting and drying) for both soils was
smaller than from calibration Methods 2 and 3 (Table 5), resulting most noticeably in an
58
underestimation o f measured effluent ctw except near the tails o f the BTCs (Fig. 1,2).
Unlike Rhoades et al. (1976), Nadler (1991) suggested that a s varies with 6 .
Calculations using our data (not shown) confirmed that improved model estimates could
be obtained by adding a variable surface conductance element to the M F model,
especially for the fine-textured Amsterdam SiCL soil. For results presented in Chapter 2,
specifying <j s as a linear f(0) for the R76 model showed a similar, although less
substantial improvement.
Application o f Laboratory Calibration Results to Field Data
Optimized MF model parameters determined from laboratory calibration
experiments, in addition to those for the R76 and R89 models (Chapter 2), were applied
to the measured field TDR Ga and 0 to generate TDR-predicted Gw at 0.15 m depth.
Spatial mean values o f measured Ga and 0 for each time step were determined from TDR
probes in three separate locations within each plot, and used to estimate plot-averaged Gw.
The Gw obtained from soil cores were also calculated as means o f measurements from
five samples taken at randomly selected locations within each plot at each sample date. A
subset o f results are presented in Figs. 3 to 7. Magnitude o f error bars for soil cores (Fig.
3-7) reflects spatial variance at the field location (Das et al., 1999).
Performance o f all three models was best in terms o f agreement with soil cores
when using parameters determined from soil column matrix experiments. Figures 3 and 6
(R76 model), and 4 and 7 (MF model) illustrate a substantial difference in estimated Gw
generated by two distinct sets o f laboratory-measured model parameters. Das et al.
59
(1999) obtained a similar underestimation o f soil core ctwwhen applying R76 model
parameters independently determined in the laboratory to the same field data described in
this study. Both Das et al. (1999) and Heimovaara et al. (1995) observed good agreement
o f MF model predicted versus field measured ctwwhen using P = 0.5 (Mualem, 1976).
Similar to our results, Heimovaara et al. (1995) applied an optimized P value (-0.40) from
a laboratory soil column experiment under transient wetness conditions that resulted in an
underestimation o f field measured a w. The discrepancy was thought to be possibly
related to differences in the magnitude o f observed flux densities between the laboratory
and field experiments (Heimovaara et al., 1995). A greater range in soil solution flux
densities was observed for the Flathead SL transient wetness soil column experiment
relative to the Flathead SL field experiment and thus could have been a contributing
factor to the variability in p observed from our experiments. However, based on our
results and on those o f Das et al. (1999), we believe that similarities in experimental
procedure primarily contributed to the result that model parameters generated from the
soil column matrix experiments resulted in Gw predictions closer to those o f soil cores,
relative to use o f parameters determined from solute BTC experiments. Heimovaara et
al. (1995) measured Gwfrom solution samplers for both laboratory and field experiments.
In both our field and soil column matrix experiments Gw was determined from aqueous
extracts, whereas salinity was measured directly from effluent fractions in the miscible
displacement experiments. As stated previously (Chapter 2), dilution procedures
involved in obtaining sample extracts may have affected the nature o f the resulting
Plot Il (150 kg N ha"1)
Plot I (300 kg N h a'1)
O Core
(,.IU SP) MD
Plot IV (0 kg N h a 1)
Plot III (75 kg N h a 1)
Day of 1996
Fig. 3 TDR estimates of aw at 0.15 m depth in Flathead SL soil using the R76 model with best fit parameters determined from
soil matrix experiments (Method 1). KNO3 hand-applied on day 170.
Plot I (300 kg N ha"1)
Plot Il (150 K g N h a '1)
O Core
LU SP)
Plot III (75 kg N h a '1)
Plot IV (0 kg N h a'1)
Day of 1996
Fig. 4 TDR estimates of
ctw at
0.15 m depth in Flathead SL soil using the R89 model with best fit parameters determined from
soil matrix experiments (Method 1). KNO3 hand-applied on day 170.
Plot Il (150 kg N h a'1)
Plot I (300 kg N h a 1)
CTw (dS m '1)
O Core
Plot IV (0 kg N h a'1)
Plot III (75 kg N h a'1)
Day of 1996
Fig. 5 TDR estimates of ow at 0.15 m depth in Flathead SL soil using the MF model with best fit parameters determined from
soil matrix experiments (Method 1). KNO3 hand-applied on day 170.
Plot Il (150 kg N h a 1)
Plot I (300 kg N h a 1)
O Core
(,.LU SP) MD
Plot IV (0 kg N h a 1)
Plot III (75 kg N h a 1)
Day of 1996
Fig. 6 TDR estimates of aw at 0.15 m depth in Flathead SL soil using the R76 model with best fit parameters determined from
transient BTC experiment (Method 2). KNO3 hand-applied on day 170.
Plot 11(150 kg N ha"1)
Plot III (75 kg N ha
Plot IV (0 kg N ha"1)
( . UI
Plot I (300 kg N ha"1)
SP) Md
Day of 1996
Fig. 7 TDR estimates of ctw at 0.15 m depth in Flathead SL soil using the MF model with best fit parameters determined from
transient BTC experiment (Method 2). KNO3 hand-applied on day 170.
65
Cra-Q-CTWrelationship. Potentially, this is a contributing factor to a systematic
underestimation o f field-measured ctw by all parameter sets determined from solute
breakthrough experiments (e.g. Fig. 6, 7). Unfortunately, we were unable to obtain soil
solution samples from the field by vacuum extraction except for sample dates near the
beginning o f the field trial. Hence, we were unable to derive a meaningful comparison
between ctw measured from solution samples and soil cores. However, in instances where
)
solution sample was collected by vacuum extraction, measured ctwwas nearly always less
than as measured from soil cores in the same plots (Das et ah, 1999: Figs. 3,4).
The MF model parameterized using laboratory soil column solute breakthrough
experiments provided better agreement with soil cores than did the R76 and R89 models
parameterized using the same experiments (e.g. Figs. 6 and 7). For the MF model, we
observed smaller changes in estimated ctw when testing a range in parameter values,
relative to varying parameters for the R76 and R89 models. We varied only (3 for the MF
model, as the retention parameters (a, m, p, 0r, 0s) were fitted to measured water
retention data for each soil. The lower ‘sensitivity’ exhibited by the MF model proved a
benefit in this case, although in the absence o f accurate retention parameters this
characteristic might be o f little practical value.
Using TDR data from steady flow experiments (obtained prior to the pulse
application when CTa was relatively stable) we found that the standard deviations
(100 <n < 267) varied from 0.0004 to 0.002 (0) and from 0.001 to 0.004 dS m '1 (CTa).
Thus the maximum uncertainty in 0 and CTa measurements due to repeatability are about
66
0.002 (0) and 0.004 dS m"1 (cra). Using these values, the predicted uncertainty
(sensitivity) to changes in <tw based on measured changes in 0 and a a should be no more
than (Wraith and Baker, 1991) 20:5(0.002) + 2°-5(0.004) = 0.0085 dS m"1, and could be as
low as 2°'5(0.0004) + 2°'5(0.001) = 0.0020 dS m '1. Combining these sensitivity estimates
with a measured calibration relationship between a w (dS m '1) and nitrate-N (ppm) for the
Flathead soil (Das et ah, 1999) results in a measurement sensitivity o f 0.20 to 0.90 ppm
for changes in soil nitrate concentration. These results suggest that TDR provides a
highly sensitive means to discern small changes in both ctw and ionic solute concentration,
under variable soil wetness. For some practical applications it may be more important to
detect changes in Gw with very high resolution than to (necessarily) estimate c w with high
absolute accuracy. For example, detection o f solute loading near the base o f the root
zone could allow land managers to schedule water and chemical inputs more efficiently.
The possibility o f experimental bias in determining the cra-0 -aw relationships based
on dilution then extraction o f solution from soils for Method I and for the field study
does not detract from the observations made in this study and in Das et al. (1999)
regarding the potential utility o f TDR for in situ field monitoring o f ionic solutes. The
fact that the pattern and magnitude o f some Cw estimates based on TDR measurements
are in good agreement with those based on independently measured c w is encouraging.
Results from this study and others (Noborio et al., 1994; Das et al., 1999) indicate that
useful estimates o f c w, particularly in coarse-textured homogenous field soils, are
achievable using TDR combined with simple conceptual models and calibration methods.
67
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CHAPTER 4
SUMMARY
Laboratory experiments were conducted to evaluate the efficacy o f three calibration
models coupled with four calibration approaches to infer a w under variably saturated soil
conditions. In addition, model coefficients optimized from laboratory procedures were
used to estimate ctw under field conditions and results were compared with a w measured
from soil core extracts. This study demonstrated the potential to obtain very good
estimates o f ctw for laboratory and field conditions, under variable wetness and ionic
concentrations, using appropriate TDR models and calibration methods. Optimization o f
R89 and MF model parameters was more tedious than for the R76 model due to their
greater mathematical complexity. While many model/calibration method combinations
provided excellent a w estimates based on comparisons to independently measured values,
dissimilar model parameters were generated for the same soils under different
experimental conditions and for different calibration methods. Some o f the systematic
discrepancy in the a a-6-o-w relationship determined from flow and soil column matrix
experiments, is explained by differences in experimental procedures for obtaining
measured <jw. Parameters obtained from transient flow experiments and using calibration
Methods 2 (optimization o f TDR 0 and <jato
G vv
measured from column effluent
fractions) and 3 (mass conservation of a solute pulse) always described the experimental
71
data from M ethod 4 (which had low variability in a w) and from steady flow experiments
(having low variability in 0) better than for the converse situation. Therefore it seems
prudent to calibrate the C3t-G-Ct w relationship under conditions having as wide a range in
variability o f a a, g w, and 0 as possible. Choosing a calibration method that will provide a
reasonable amount o f variability in a a, 0, and ctw should also minimize the potential for
obtaining non-unique parameters for both the R76 and R89 models. Alternative
functional forms for T(0) in R76 and Gws in R89 models might also potentially provide a
useful means to address the issue o f non-unique model parameters.
This study and the related work o f Das et al. (1999) indicated that the selection o f
appropriate calibration techniques is at least as important to obtaining reliable estimates
o f G w with TDR as is the chosen calibration model. The best estimates o f G w for the
Flathead field soil were obtained using model (R76, R89, MF) parameters derived from
calibration Method I (soil column matrix), presumably due to similar techniques used to
measure
Gw
in each case. Because o f this potential procedural artifact, we are not
confident in the universality o f our findings that the factorial soil column matrix is the
superior laboratory calibration method for application to field measurements. Calibration
relationships determined based on agreement with
Gw
are useful only if the baseline
measurements are accurate. Additional research is needed to evaluate the agreement and
accuracy o f different techniques used to measure baseline
Gw
in soils.
Based on results o f the three models analyzed in this study, it seems likely that the
conductor-based models (R76, R89) may be better suited to use with heavier textured
72
soils than is the MF model. Adding a surface conductance (<ts) element to the MF model
could potentially improve crw estimates for finer textured soils. In accordance with
Heimovaara et al. (1995), results indicated that fitting the (3 parameter in the MF model
(rather than assuming (3 = 0.5; Mualem 1976) improved TDR
Ow
estimates. The MF
model is potentially as effective as the conductor based models (R76, R89) for use with
coarse textured soils, has only one fitting parameter (other than for the chosen soil water,
retention model) compared to three for the R76 and R89 models, and Gw estimates appear
to be less sensitive to changes in this (|3) parameter than for some o f the parameters in the
R76 and R89 models.
Preliminary results (not shown) from this study also suggest that specifying
Gs
as a
variable function o f 0 should improve model estimates o f G w , especially for fine-textured
soils and under conditions o f extreme transient soil wetness. The trade-off between an
additional level o f empiricism and improved model performance could prove worthwhile.
Additional work is needed to help clarify the relationships between
g
s,
0, and G w .
MONTANA STATE UNIVERSITY - BOZEMAN
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